New filter, water, and stress concerns

[meisabelep]

Hi,
I have questions about fixing up a tank that already has a fish in it - adding more water and a first-time filter without stress.

I accidentally acquired a sweet Fantail Goldfish recently and Himsher is my new best friend, but I also depend on my mom and she's "had fish her whole life" so of course she "knows everything" and setting things up correctly has been a struggle.
Please don't judge me for the bad tank conditions I do love this fish.

Anyway,
Fishy is in a 10 gallon tank with pretty dirty water (first filter I convinced my mom to buy was broken, took a while to convince her to let me get a new one.)

I installed the filter and Himsher didn't seem too stressed. I ran it for a moment and realized that I need about 2 more inches of water in the tank, so I turned it off. (about an hour ago - 1:45pm EST)

Main Questions:
Should I wait a while to add more water? Add it all at once? or bit by bit?
Should I let fishy chill after adding water and before turning the filter on?
The water is pretty dirty, but the tank hasn't been cycled, so should I keep all of the dirty water in there for a while before changing some of it?
-- I have stress coat for the water - and it's from a well, but I do not have any test strips (not my choice)

I know I have more questions but my mind just blanked. Any advice, thoughts, or answers are appreciated. It doesn't have to be specific to this.

Fishy seems fine, I'm sitting next to the tank in case that helps with stress. I know Himsher is lonely and I hope we will get another fish friend soon - when tank conditions are good.
I promise that I am not trying to be a bad fish friend. I have done so much research, I am just currently extra dependent on my mom. She's not bad, she just shuts down some of the things I've learned and she doesn't want to "waste money" but Himsher is a family member now. We're working on it.

Thanks for your time/help/whatever. Sorry this is so long (could've been longer, haha)
I wish you all the best!

[gone fishin]

Sorry to say but this site is for saltwater fish. It has been many years since I kept a freshwater tank, so I will not be of much help to you. The only thing I would suggest is getting your tank cycled before adding any fish to it.

[meisabelep]

Originally Posted by gone fishin

Sorry to say but this site is for saltwater fish. It has been many years since I kept a freshwater tank, so I will not be of much help to you. The only thing I would suggest is getting your tank cycled before adding any fish to it.

Thanks. I feel a bit embarrassed. I guess I wasn't paying enough attention to the "reef central" part, hahaha.
This seems like a friendly and helpful community. I think I found a helpful freshwater community.